To solve for \( y \) in terms of \( x \) from the equation \( 3x + 4y = 7 \), we will isolate \( y \).
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Start with the original equation:
\[ 3x + 4y = 7 \]
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Subtract \( 3x \) from both sides:
\[ 4y = 7 - 3x \]
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Now, divide both sides by 4:
\[ y = \frac{7 - 3x}{4} \]
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We can rewrite this as:
\[ y = -\frac{3}{4}x + \frac{7}{4} \]
Now, let's examine the options:
A. \( y = 3x + 7 \) - This is incorrect.
B. \( y = -\frac{3}{4}x + 7 \) - This is incorrect because the constant term should be \( \frac{7}{4} \).
C. \( y = -\frac{3}{4}x + \frac{7}{4} \) - This is correct.
So the solution for \( y \) in terms of \( x \) is:
\[ \boxed{C} \]
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